Damage identification in a parabolic arch by means of natural frequencies, modal shapes and curvatures

This paper investigates damage identification techniques based on the difference of modal frequencies, shapes and curvatures in the damaged and undamaged states of the structure. The sensitivity of the identification algorithm with respect to damage parameters is discussed and the minimum number of measured quantities to identify the damage is assessed. It is shown that modal curvatures can be effectively used to pre-localise the damage and to add a penalty term in the objective function which weighs the difference between natural frequencies and modal displacements. Such a term improves the local convexity of the objective function and enhances the convergence rate of the minimization algorithm. The procedure is validated against the results of the experiments on a parabolic arch carried out by the authors. The advantages of such an approach compared to techniques solely based on frequencies are that the ill-conditioning of the inverse problem is reduced and a more accurate estimate of the damage parameters is achieved.